Page 259 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math15-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

bdkbZ fuf'pr lekdyu

 x  3 a a 3 2 uksV
-  ax − 2 = a −  3 − 0 = & mÙkj

 3   0  3 3

∫ a dx
mnkgj.k 7- 0 dk eku Kkr dhft,A
a 2 − x 2

a
1 x 

∫ a dx
 sin − 
gy % 0 a − x 2    0
a

2
0
a
 

-

 2


a
a
 
π π
-

2

3 - 2 3 - mÙkj

2 2
mnkgj.k 8- ∫ 0 π/2 x cos x dk eku Kkr dhft,A
gy % [k.M'k% lekdyu }kjk
∫ 0 π /2 x cos x ! - [ x ] sin x π 0 /2 − ∫ 0 π /2 sin x dx
 π π  π / 2
-  sin − 0 2 [  − ] cos x
 2 2  0
π  π  π π
- +  cos − cos 0 - + 0 − 1 = 2 mÙkj

2  2  2 2
mnkgj.k 9- ∫ π/4 1 − sin2x dk eku Kkr dhft,A
0

gy % ∫ π /4 1 − sin 2x ! - ∫ π /4 cos x + 2 sin x − 2 2 sin x cos x !
0 0

2
- ∫ π /4 (cosx − sin ) !
x
0
- ∫ π /4 (cosx − sin ) !
x
0
- [ cosx ]sin x + π 0 / 4

π  π 
- sin + cos  2

3P 2
3P

 4 4 
 1 1 
-  +  2 3 2
 2 2 
2
- / - (2 + 1) mÙkj
2